Einstein’s cosmic model of 1931 revisited: an analysis and translation of a forgotten model of the universe

Abstract

We present an analysis and translation of Einstein’s 1931 paper “Zum
kosmologischen Problem der allgemeinen Relativitätstheorie” or “On the
cosmological problem of the general theory of relativity”. In this little-known
paper, Einstein proposes a cosmic model in which the universe undergoes an expansion
followed by a contraction, quite different to the monotonically expanding Einstein-de
Sitter model of 1932. The paper offers many insights into Einstein’s cosmology in the
light of the first evidence for an expanding universe and we consider his views of issues
such as the curvature of space, the cosmological constant, the singularity and the
timespan of the expansion. A number of original findings concerning Einstein’s 1931 model
are presented. We find that Einstein’s calculations of the present radius and matter
density of the universe contain some anomalies: we suggest that his estimate of the age of
the universe is based on a questionable calculation of Friedmann’s: we find that the model
is not periodic, contrary to what is often stated. A first English translation of
Einstein’s paper is included as an Appendix.

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